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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 17:52:47 +0000Lagrangian coherent structures in the planar elliptic restricted three-body problem
https://resolver.caltech.edu/CaltechAUTHORS:20090417-120127476
Authors: Gawlik, Evan S.; Marsden, Jerrold E.; Du Toit, Philip; Campagnola, Stefano
Year: 2009
DOI: 10.1007/s10569-008-9180-3
This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP), a generalization of the circular restricted three-body problem (CR3BP) that asks for the motion of a test particle in the presence of two elliptically orbiting point masses. Previous studies demonstrate that an understanding of transport phenomena in the CR3BP, an autonomous dynamical system (when viewed in a rotating frame), can be obtained through analysis of the stable and unstable manifolds of certain periodic solutions to the CR3BP equations of motion. These invariant manifolds form cylindrical tubes within surfaces of constant energy that act as separatrices between orbits with qualitatively different behaviors. The computation of LCS, a technique typically applied to fluid flows to identify transport barriers in the domains of time-dependent velocity fields, provides a convenient means of determining the time-dependent analogues of these invariant manifolds for the ER3BP, whose equations of motion contain an explicit dependency on the independent variable. As a direct application, this study uncovers the contribution of the planet Mercury to the Interplanetary Transport Network, a network of tubes through the solar system that can be exploited for the construction of low-fuel spacecraft mission trajectories.https://authors.library.caltech.edu/records/zxsnm-88k85Flybys in the planar, circular, restricted, three-body problem
https://resolver.caltech.edu/CaltechAUTHORS:20130111-105519900
Authors: Campagnola, Stefano; Skerritt, Paul; Russell, Ryan P.
Year: 2012
DOI: 10.1007/s10569-012-9427-x
An analysis is presented of gravity assisted flybys in the planar, circular, restricted three-body problem (pcr3bp) that is inspired by the Keplerian map and by the Tisserand- Poincaré graph. The new Flyby map is defined and used to give insight on the flyby dynamics and on the accuracy of the linked-conics model. The first main result of this work is using the Flyby map to extend the functionality of the Tisserand graph to low energies beyond the validity of linked conics. Two families of flybys are identified: Type I (direct) flybys and Type II (retrograde) flybys. The second main result of this work shows that Type I flybys exist at all energies and are more efficient than Type II flybys, when both exist. The third main result of this work is the introduction of a new model, called "Conics, When I Can", which mixes numerical integration and patched conics formulas, and has applications beyond the scope of this work. The last main result is an example trajectory with multiple flybys at Ganymede, all outside the linked-conics domain of applicability. The trajectory is computed with the pcr3bp, and connects an initial orbit around Jupiter intersecting the Callisto orbit, to an approach transfer to Europa. Although the trajectory presented has similar time of flight and radiation dose of other solutions found in literature, the orbit insertion Δv is 150 m/s lower. For this reason, the transfer is included in the lander option of the Europa Habitability Mission Study.https://authors.library.caltech.edu/records/2sfsk-cks41